Do you mean some Text on the image and that Text will show up when printed?
Placing the Date and maybe the Time, that is the Camera's Time, on the image when it was taken was a feature of some cameras, not all. It was more of a gimmick and soon faded away. There might still be some cameras that offer that option. I personally would never use it as it is just a distraction to what the real subject of the image is.
I don't think there is any method of doing this except manually with either a Watermark, LR, or adding Text to the image in PS.
The actual Capture Date and Time is part of all digital images and unless stripped will follow the image. That is except when you are making a Hard Copy of it, IE Printing it out.
Learn something new every day. Thanks Bob.